The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A326029 Number of strict integer partitions of n whose mean and geometric mean are both integers. 8
 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 3, 1, 2, 1, 3, 1, 1, 2, 3, 1, 3, 1, 1, 3, 6, 1, 3, 1, 2, 1, 1, 1, 3, 1, 6, 1, 5, 1, 2, 2, 2, 4, 3, 1, 9, 1, 1, 3, 1, 1, 4, 1, 4, 2, 6, 1, 6, 1, 3, 7, 4, 2, 5, 1, 10, 1, 3, 1, 9, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,11 LINKS Table of n, a(n) for n=0..85. Wikipedia, Geometric mean EXAMPLE The a(55) = 2 through a(60) = 9 partitions: (55) (56) (57) (58) (59) (60) (27,16,9,2,1) (24,18,8,6) (49,7,1) (49,9) (54,6) (27,25,5) (50,8) (48,12) (27,18,12) (27,24,9) (27,24,6,2,1) (36,12,9,2,1) (36,9,6,4,3,2) (24,18,9,6,2,1) (27,16,9,4,3,1) MATHEMATICA Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&IntegerQ[Mean[#]]&&IntegerQ[GeometricMean[#]]&]], {n, 0, 30}] CROSSREFS Partitions with integer mean and geometric mean are A326641. Strict partitions with integer mean are A102627. Strict partitions with integer geometric mean are A326625. Non-constant partitions with integer mean and geometric mean are A326641. Subsets with integer mean and geometric mean are A326643. Heinz numbers of partitions with integer mean and geometric mean are A326645. Cf. A051293, A067538, A067539, A078175, A082553, A316413, A326027, A326623, A326644, A326646, A326647. Sequence in context: A074298 A356097 A356096 * A356167 A176028 A031246 Adjacent sequences: A326026 A326027 A326028 * A326030 A326031 A326032 KEYWORD nonn AUTHOR Gus Wiseman, Jul 16 2019 EXTENSIONS More terms from Jinyuan Wang, Jun 26 2020 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 7 01:49 EST 2023. Contains 367616 sequences. (Running on oeis4.)